Language-goal aerial navigation is a critical challenge in embodied AI, requiring UAVs to localize targets in complex environments such as urban blocks based on textual specification. Existing methods, often adapted from indoor navigation, struggle to scale due to limited field of view, semantic ambiguity among objects, and lack of structured spatial reasoning. In this work, we propose GeoNav, a geospatially aware multimodal agent to enable long-range navigation. GeoNav operates in three phases-landmark navigation, target search, and precise localization-mimicking human coarse-to-fine spatial strategies. To support such reasoning, it dynamically builds two different types of spatial memory. The first is a global but schematic cognitive map, which fuses prior textual geographic knowledge and embodied visual cues into a top-down, annotated form for fast navigation to the landmark region. The second is a local but delicate scene graph representing hierarchical spatial relationships between blocks, landmarks, and objects, which is used for definite target localization. On top of this structured representation, GeoNav employs a spatially aware, multimodal chain-of-thought prompting mechanism to enable multimodal large language models with efficient and interpretable decision-making across stages. On the CityNav urban navigation benchmark, GeoNav surpasses the current state-of-the-art by up to 12.53% in success rate and significantly improves navigation efficiency, even in hard-level tasks. Ablation studies highlight the importance of each module, showcasing how geospatial representations and coarse-to-fine reasoning enhance UAV navigation.